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Boundary layer formulations in orthogonal curvilinear coordinates for flow over wind-generated surface waves

Published online by Cambridge University Press:  06 February 2020

Kianoosh Yousefi Open the ORCID record for Kianoosh Yousefi [Opens in a new window]  and
Fabrice Veron Open the ORCID record for Fabrice Veron [Opens in a new window]
Kianoosh Yousefi*
Affiliation:
Department of Mechanical Engineering, University of Delaware, Newark, DE19716, USA School of Marine Science and Policy, University of Delaware, Newark, DE19716, USA
Fabrice Veron
Affiliation:
School of Marine Science and Policy, University of Delaware, Newark, DE19716, USA
*
†Email address for correspondence: kyousefi@udel.edu
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Abstract

The development of the governing equations for fluid flow in a surface-following coordinate system is essential to investigate the fluid flow near an interface deformed by propagating waves. In this paper, the governing equations of fluid flow, including conservation of mass, momentum and energy balance, are derived in an orthogonal curvilinear coordinate system relevant to surface water waves. All equations are further decomposed to extract mean, wave-induced and turbulent components. The complete transformed equations include explicit extra geometric terms. For example, turbulent stress and production terms include the effects of coordinate curvature on the structure of fluid flow. Furthermore, the governing equations of motion were further simplified by considering the flow over periodic quasi-linear surface waves wherein the wavelength of the disturbance is large compared to the wave amplitude. The quasi-linear analysis is employed to express the boundary layer equations in the orthogonal wave-following curvilinear coordinates with the corresponding decomposed equations for the mean, wave and turbulent fields. Finally, the vorticity equations are also derived in the orthogonal curvilinear coordinates in order to express the corresponding velocity–vorticity formulations. The equations developed in this paper proved to be useful in the analysis and interpretation of experimental data of fluid flow over wind-generated surface waves. Experimental results are presented in a companion paper.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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